A mathematical model for networks with structures in the mesoscale

TL;DR

This paper introduces a multilevel network model capturing mesoscale structures in complex systems, extending existing models and analyzing their properties to better understand real-world networks like social and transportation systems.

Contribution

The paper presents a novel multilevel network model that generalizes hyper-network models, capturing mesoscale structures in complex systems and analyzing their structural properties.

Findings

Multilevel networks effectively model mesoscale structures.

Analytical relationships between efficiency, clustering, and underlying networks.

Random models show similar underlying networks can have different mesoscale structures.

Abstract

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which generalizes the hyper-network and hyper-structure models, fits perfectly with several real-life complex systems, including social and public transportation networks. We present an analysis of the structural properties of the multilevel network, including the clustering and the metric structures. Some analytical relationships amongst the efficiency and clustering coefficient of this new model and the corresponding parameters of the underlying network are obtained. Finally some random models for multilevel networks are given to illustrate how different multilevel structures can produce similar underlying networks and therefore that the mesoscale structure should be taken into account in many applications.